Respuesta :
Answer:
2.0 mph
Step-by-step explanation:
Considering a straight-line displacement, the current has a velocity acting on the same axis at which the motorboat is traveling. Assume that the current's velocity is positive in the downstream leg of the trip, the velocity of the current can be determined by:
[tex]U: (V_{boat} - V_{current})*t_U=12\\D: (V_{boat} + V_{current})*t_D=12\\t_U +t_D = 2.5 = \frac{12}{10 - V_{current}}+\frac{12}{10 + V_{current}}\\2.5*(10^2-V_{current}^2)=120 -12V_{current}+120+12V_{current}\\-2.5V_{current}^2 +250 = 240\\V_{current}=\sqrt{\frac{10}{2.5}}\\V_{current} = 2\ mph[/tex]
The speed of the current is 2 miles per hour.
Answer: the speed of the current is 202 mph
Step-by-step explanation:
Let x represent the speed of the current.
Miles travelled while going upstream is 1212
Miles travelled while going downstream is 1212
Assuming the motor boat travelled against the wind while going upstream, the speed would be
(1010 - x) mph
Assuming the motor boat travelled with the wind while going downstream, the speed would be
(1010 + x) mph
Distance = speed × time
Time = distance/speed
Time it took upstream is
1212/(1010 - x)
Time it took downstream is
1212/(1010 + x)
Total time for the trip is 1.5 hours. It means that
1212/(1010 - x) + 1212/(1010 + x) = 2.5
Cross multiplying by (1010 -x)(1010 + x), it becomes
1212(1010 + x) + 1212(1010 - x) =
2.5(1010 - x)(1010 + x)
1224120 + 1212x + 1224120 - 1212x = 2.5(1020100 + 1010x - 1010x - x²)
2448240 = 2550250 - 2.5x²
2.5x² = 102010
x² = 102010/2.5
x² = 40804
x = √40804
x = 202 mph
